Bounding errors introduced by clustering of customers in closed product-form queuing networks

Journal of the ACM

Volumn 43, Issue 4, 1996, Pages 641-669

  Cheng, William C ^a,b   Muntz, Richard R ^a,c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b University of California ^*  (United States)

^c Department of Civil and Environmental Engineering   (United States)

Author keywords

Algorithms; Balance equation; Closed network; Clustering; Error bound; Product form; Quasi reversibility; Queuing network; Theory

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; ERRORS; MARKOV PROCESSES; PERFORMANCE; PROBABILITY; QUEUEING THEORY;

BALANCE EQUATIONS; CLOSED PRODUCT FORM QUEUING NETWORKS; CLUSTERING; ERROR BOUND; QUASI REVERSIBILITY;

COMPUTER NETWORKS;

EID: 0030197367     PISSN: 00045411     EISSN: None     Source Type: Journal    
DOI: 10.1145/234533.234539     Document Type: Article

References (34)

1. ARTIS, H. P. 1985. Workload characterization using SAS PROC FASTCLUS. In Workload Characterization of Computer Systems and Computer Networks, G. Serazzi, Ed. North-Holland, Amsterdam, The Netherlands, pp. 21-32.
2. AURENHAMMER, F. 1991. Voronoi diagrams - A survey of a fundamental geometric data structure. ACM Comput. Surv. 23, 3 (Sept.), 345-405.
3. BARD, Y. 1979. Some extensions to multiclass queueing network analysis. In Performance of Computer Systems, M. Arato, A. Butrimenko, and E. Gelenbe, Eds. North-Holland, Amsterdam, The Netherlands, pp. 51-61.
4. BASKETT, F., CHANDY, K. M., MUNTZ, R. R., AND PALACIOS, F. 1975. Open, closed and mixed networks of queues with different classes of customers. J. ACM 22, 2 (Apr.), 248-260.
5. BAZARAA, M. S., AND SHETTY, C. M. 1979. Nonlinear Programming: Theory and Algorithms. Wiley, New York.
6. BERTSEKAS, D. P. 1987. Dynamic Programming: Deterministic and Stochastic Models. Prentice-Hall, Englewood Cliffs, N. J.
7. CHANDY, K. M., HOWARD, JR., J. H., AND TOWSLEY, D. F. 1977. A characterization of product-form queueing networks. J. ACM 24, 2 (Apr.), 250-263.
8. CHANDY, K. M., AND NEUSE, D. 1982. Linearizer: A heuristic algorithm for queueing network models of computer systems. Commun. ACM 25, 126-134.
9. CHENG, W. C. 1992. Optimization, Performance Bounds, and Approximations in Queueing Networks. Ph.D. Dissertation. Univ. California at Los Angeles, Los Angeles, Calif., July.
10. CHENG, W. C., AND MUNTZ, R. R. 1991. Optimal routing for closed queueing networks. Perf. Eval. 13, 1 (Sept.), 3-17.
11. COURTOIS, P. J. 1977. Decomposability - Queueing and Computer System Applications. Academic Press, New York.
12. COX, D. R. 1955. A use of complex probabilities in the theory of stochastic processes. In Cambridge Phil. Soc. Vol. 51, pp. 313-319.
13. DERMAN, S. 1970. Finite State Markovian Decision Processes. Academic Press, New York.
14. DE SOUZA E SILVA, E., AND LAVENBERG, S. S. 1989. Calculating joint queue length distributions in product form queueing networks. J. ACM 36, 1 (Jan.), 194-207.
15. DE SOUZA E SILVA, E., LAVENBERG, S. S., AND MUNTZ, R. R. 1984. A perspective on iterative methods for the approximate analysis of closed queueing networks. In Mathematical Computer Performance and Reliability. G. Iazeola, P. J. Courtois, and A. Hordijk, Eds. North Holland, Amsterdam, The Netherlands, pp. 225-244.
16. DE SOUZA E SILVA, E., LAVENBERG, S. S., AND MUNTZ, R. R. 1986. A clustering approximation technique for queueing network models with a large number of chains. IEEE Trans. Comput. C-35, 419-430.
17. DOWDY, L. W., CARLSON, B. M., KRANTZ, A. T., AND TRIPATHI, S. K. 1992. Single-class bounds of multi-class networks. J. ACM 39, 1 (Jan.), 188-213.
18. HSIEH, C. T., AND LAM, S. S. 1989. PAM - A noniterative approximate solution method for closed multichain queueing networks. Perf. Eval. 9, 119-133.
19. KELLY, F. P. 1979. Reversibility and Stochastic Networks. Wiley, New York.
20. LAVENBERG, S. S., AND REISER, M. 1980. Stationary state probabilities of arrival instants for closed queueing networks with multiple types of customers. J. Appl. Prob. 17, 1048-1061.
21. MACQUEEN, J. B. 1967. Some methods for classification and analysis of multivariate observations. In Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability.
22. MOORE, F. R. 1962. Computational model of a closed queueing network with exponential servers. IBM J. Res. Dev. 16, 567-572.
23. MUNTZ, R. R. 1972. Poisson departure processes and queueing networks. Tech. Rep. RC 4145. IBM Thomas J. Watson Research Center, Yorktown Heights, N. Y.
24. NELSON, R. D. 1993. The mathematics of product form queuing networks. ACM Comput. Surv. 25, 3 (Sept.), 339-369.
25. REISER, M. 1981. Mean-value analysis and convolution method for queue-dependent servers in closed queueing networks. Perf. Eval. 1, 7-18.
26. REISER, M., AND KOBAYASHI, H. 1975. Queueing networks with multiple closed chains: Theory and computational algorithms. IBM J. Res. Dev. 19, 283-294.
27. REISER, M., AND LAVENBERG, S. S. 1980. Mean-value analysis of closed multichain queuing networks. J. ACM 27, 313-322.
28. SCHWEITZER, P. 1979. Approximate analysis of multiclass closed networks of queues. In Proceedings of the International Conference on Stochastic Control and Optimization (Amsterdam, The Netherlands).
29. SEBER, G. A. F. 1984. Multivariate Observations. Wiley, New York.
30. TRIPATHI, S. K., AND DOWDY, L. W. 1985. Workload representation and its impact on the performance prediction using queueing network models. In Workload Characterization of Computer Systems and Computer Networks, G. Serazzi, Ed. North-Holland, Amsterdam, The Netherlands, pp. 159-178.
31. TRIPATHI, S. K., AND WOODSIDE, C. M. 1988. A vertex-allocation theorem for resources in queueing networks. J. ACM 35, 1 (Jan.), 221-230.
32. WILLIAMS, A. C., AND BHANDIWAD, R. A. 1976. A generating function approach to queueing network analysis of multiprogrammed computers. Networks 6, 1-22.
33. ZAHORJAN, J. 1980. The approximate solution of large queuing network models. Tech. Rep. Ph.D. Dissertation. Univ. Toronto, Toronto, Ont., Canada.
34. ZAHORJAN, J., EAGER, D. E., AND SWEILLAM, H. M. 1988. Accuracy, speed, and convergence of approximate mean value analysis. Perf. Eval. 8, 255-270.